The increasing complexity of modern software systems necessitates robust autonomic self-management capabilities. While Large Language Models (LLMs) demonstrate potential in this domain, they often face challenges in adapting their general knowledge to specific service contexts. To address this limitation, we propose ServiceOdyssey, a self-learning agent system that autonomously manages microservices without requiring prior knowledge of service-specific configurations. By leveraging curriculum learning principles and iterative exploration, ServiceOdyssey progressively develops a deep understanding of operational environments, reducing dependence on human input or static documentation. A prototype built with the Sock Shop microservice demonstrates the potential of this approach for autonomic microservice management.